Distributed Adaptive Networks: A Graphical Evolutionary Game-Theoretic View

Distributed adaptive filtering has been considered as an effective approach for data processing and estimation over distributed networks. Most existing distributed adaptive filtering algorithms focus on designing different information diffusion rules, regardless of the nature evolutionary characteristic of a distributed network. In this paper, we study the adaptive network from the game theoretic perspective and formulate the distributed adaptive filtering problem as a graphical evolutionary game. With the proposed formulation, the nodes in the network are regarded as players and the local combiner of estimation information from different neighbors is regarded as different strategies selection. We show that this graphical evolutionary game framework is very general and can unify the existing adaptive network algorithms. Based on this framework, as examples, we further propose two error-aware adaptive filtering algorithms. Moreover, we use graphical evolutionary game theory to analyze the information diffusion process over the adaptive networks and evolutionarily stable strategy of the system. Finally, simulation results are shown to verify the effectiveness of our analysis and proposed methods.Comment: Accepted by IEEE Transactions on Signal Processin

Ligand exchange reactions of [Re₂(μ-OR)₃(CO)₆]⁻(R = H, Me) with sulfur, selenium, phosphorus and nitrogen donor ligands, investigated by electrospray mass spectrometry

Negative-ion electrospray mass spectrometry has been used to investigate the reactions of the dinuclear rhenium aggregates [Re₂(μ-OH)₃(CO)₆]⁻ 1 and [Re₂(μ-OMe)₃(CO)₆]⁻ 2 with a range of thiols, benzeneselenol, and some other sulfur-, phosphorus- and nitrogen-based ligands. Typically up to three of the hydroxo ligands are replaced by simple thiolates, giving the series of species [Re₂(OH)₂(SR)(CO)₆]⁻, [Re₂(OH)(SR)₂(CO)₆]⁻, and [Re₂(SR)₃(CO)₆]⁻. Similarly, reaction of 1 with H₂S gives the species [Re₂(μ-SH)₃(CO)₆]⁻, which undergoes an analogous fragmentation process to [Re₂(μ-OH)₃(CO)₆]⁻, at high cone voltages, by loss of H₂S and formation of [Re₂(S)(SH)(CO)₆]⁻. With ligands which are good chelating agents (such as dithiocarbamates R₂NCS₂⁻, and thiosalicylic acid, HSC₆H₄CO₂H) initial substitution of one or two OH groups readily occurs, but on standing the dimer is cleaved giving [Re(S₂CNR₂)₂(CO)₃]⁻ and [Re(SC₆H₄CO₂)(CO)₃]⁻. The different reactivities of the dithiol reagents benzene-1,2- and benzene-1,4-dimethanethiol towards 1 are also described. Complex 1 also reacts with aniline, and with primary (but not secondary) amides RC(O)NH₂, giving monosubstituted species [Re₂(OH)₂(NHPh)(CO)₆]⁻ and [Re₂(OH)₂{NHC(O)R}(CO)₆]⁻ respectively. The reactions with adenine and thymine, and with the inorganic anions thiocyanate and thiosulfate, are also described